Systematic Parallel Line Design

What spacing would you select for this design? What is the maximum trackline length for the design you have selected? What on-effort line length are we likely to achieve?

The spacing chosen by dssd of 4937.5 m to generate a line length of 200 km resulted in a maximum trackline length of around 261 km (each exact answer will vary due to the random generate of surveys). If we choose this design then it is possible that when we randomly generate our survey we may not be able to complete it with the effort we have available.

We should therefore increase the spacing between the transects and re-run the coverage simulations. A spacing of 5000 m gave a maximum trackline length of around 249 km (see summary table of Trackline length in the output below) so we can be fairly confident that we will be able to complete any survey which we randomly generate from this design. This spacing should allow us to achieve an on-effort line length of 199 km (see Line length section of design summary below). The minimum line length we would expect to achieve is 184 km and the maximum is 206 km. [Note your values might differ slightly to those below]

# Define the design
design.space500 <- make.design(region = region,
                      transect.type = "line",
                      design = "systematic",
                      spacing = 5000,
                      design.angle = 90,
                      edge.protocol = "minus",
                      truncation = 2000,
                      coverage.grid = cover)

# Run the coverage simulation
design.space500 <- run.coverage(design.space500, reps = 100, quiet=TRUE)
plot(design.space500)

Coverage grid plot for parallel design.

# Display the design statistics
design.space500

## 
##    Strata St Andrews Bay:
##    _______________________
## Design:  systematically spaced transects
## Spacing:  5000
## Number of samplers:  NA
## Line length: NA
## Design angle:  90
## Edge protocol:  minus
## 
## Strata areas:  987500079
## Region and effort units:  m
## Coverage Simulation repetitions:  100
## 
##     Number of samplers:
##     
##         St Andrews Bay Total
## Minimum            7.0   7.0
## Mean               7.9   7.9
## Median             8.0   8.0
## Maximum            8.0   8.0
## sd                 0.3   0.3
## 
##     Covered area:
##     
##         St Andrews Bay     Total
## Minimum      726723508 726723508
## Mean         762395980 762395980
## Median       767998725 767998725
## Maximum      778529244 778529244
## sd            16151280  16151280
## 
##     % of region covered:
##     
##         St Andrews Bay Total
## Minimum          73.59 73.59
## Mean             77.20 77.20
## Median           77.77 77.77
## Maximum          78.84 78.84
## sd                1.64  1.64
## 
##     Line length:
##     
##         St Andrews Bay     Total
## Minimum      184499.71 184499.71
## Mean         197696.89 197696.89
## Median       199089.69 199089.69
## Maximum      205653.53 205653.53
## sd             6091.82   6091.82
## 
##     Trackline length:
##     
##         St Andrews Bay     Total
## Minimum      220587.91 220587.91
## Mean         242551.69 242551.69
## Median       246354.84 246354.84
## Maximum      248652.26 248652.26
## sd             8894.84   8894.84
## 
##     Cyclic trackline length:
##     
##         St Andrews Bay     Total
## Minimum      252047.90 252047.90
## Mean         279222.83 279222.83
## Median       283882.44 283882.44
## Maximum      285872.40 285872.40
## sd            10523.92  10523.92
## 
##     Coverage Score Summary:
##     
##         St Andrews Bay      Total
## Minimum     0.33000000 0.33000000
## Mean        0.77214286 0.77214286
## Median      0.80000000 0.80000000
## Maximum     0.88000000 0.88000000
## sd          0.09151095 0.09151095

Equal Spaced Zigzag Design

Does this design meet our survey effort constraint? What is the maximum total trackline length for this design? What line length are we likely to achieve with this design? Is this higher or lower than the systematic parallel design?

You were asked to then run a coverage simulation and check if the trackline length was within our effort constraints. I found the maximum trackline length to be 242 km (see Trackline length summary table in the output below) so within our constraint of 250 km. I then got a mean line length of 221 km and minimum and maximum line lengths of 212 km and 227 km, respectively (see Line length summary table in the output below). We can therefore expect to achieve just over 20 km more on-effort survey line length with the zigzag design than the systematic parallel line design - that is a 10% gain! [Note your values may differ slightly]

design.zz.4500 <- make.design(region = region,
                      transect.type = "line",
                      design = "eszigzag",
                      spacing = 4500,
                      design.angle = 0,
                      edge.protocol = "minus",
                      bounding.shape = "convex.hull",
                      truncation = 2000,
                      coverage.grid = cover)

# Run coverage simulation
design.zz.4500 <- run.coverage(design.zz.4500, reps = 100, quiet=TRUE)
# Plot coverage
plot(design.zz.4500)

Coverage grid plot for zigzag design.

## 
##    Strata St Andrews Bay:
##    _______________________
## Design:  equal spaced zigzag
## Spacing:  4500
## Number of samplers:  NA
## Line length: NA
## Design angle:  0
## Edge protocol:  minus
## 
## Strata areas:  987500079
## Region and effort units:  m
## Coverage Simulation repetitions:  100
## 
##     Number of samplers:
##     
##         St Andrews Bay Total
## Minimum            9.0   9.0
## Mean               9.7   9.7
## Median            10.0  10.0
## Maximum           10.0  10.0
## sd                 0.5   0.5
## 
##     Covered area:
##     
##         St Andrews Bay     Total
## Minimum      814702426 814702426
## Mean         849106812 849106812
## Median       849282679 849282679
## Maximum      877852116 877852116
## sd            14208738  14208738
## 
##     % of region covered:
##     
##         St Andrews Bay Total
## Minimum          82.50 82.50
## Mean             85.99 85.99
## Median           86.00 86.00
## Maximum          88.90 88.90
## sd                1.44  1.44
## 
##     Line length:
##     
##         St Andrews Bay     Total
## Minimum      211634.28 211634.28
## Mean         221537.85 221537.85
## Median       222855.88 222855.88
## Maximum      227236.61 227236.61
## sd             4127.56   4127.56
## 
##     Trackline length:
##     
##         St Andrews Bay     Total
## Minimum      215427.11 215427.11
## Mean         231041.17 231041.17
## Median       230342.94 230342.94
## Maximum      241615.46 241615.46
## sd             5982.13   5982.13
## 
##     Cyclic trackline length:
##     
##         St Andrews Bay     Total
## Minimum      254779.09 254779.09
## Mean         271160.55 271160.55
## Median       271102.41 271102.41
## Maximum      282601.86 282601.86
## sd             6123.11   6123.11
## 
##     Coverage Score Summary:
##     
##         St Andrews Bay     Total
## Minimum      0.2500000 0.2500000
## Mean         0.8595858 0.8595858
## Median       0.8900000 0.8900000
## Maximum      1.2200000 1.2200000
## sd           0.1024669 0.1024669

Do you think the coverage scores look uniform across the study region? Where are they higher/lower? Why do you think this is?

You were finally asked to look at the coverage scores across the survey region to see if this design has even coverage. There are some points with lower coverage around the survey region boundary. This is actually down to the fact we are using a minus sampling strategy. If we plotted coverage scores from a systematic parallel design we would see a similar pattern. Usually edge effects from minus sampling are minor unless we have a very long survey region boundary containing a small study area. If the fact that we are using a zigzag design was causing us issues with coverage we would expect to see higher coverage at the very top or very bottom of the survey region (as our design angle is 0). We do not see this. The survey region boundaries at the top and bottom are both quite wide and perpendicular to the design angle, in this situation zigzag designs perform well with regard to even coverage.

Coverage

The next step is to set up a coverage grid. A coverage grid is a grid of regularly spaced points and is used to assess whether each point in the survey region is equally likely to sampled. The coverage grid needs to be created before the coverage simulation is run.

# Set up coverage grid, with lots of grid points
#     This many grid points will slow down execution of this code;
#     I used this resolution to see fine detail in the plots for demonstration
#     If you adapt this code for your use, you may wish to initially reduce points
cover.tm <- make.coverage(region.tm, n.grid.points = 5000)
design.tm <- make.design(region = region.tm,
                         transect.type = "point",
                         design = "systematic",
                         samplers = c(25,15),
                         design.angle = 0,
                         edge.protocol = "minus",
                         truncation = 100,
                         coverage.grid = cover.tm)
survey.tm <- generate.transects(design.tm)

survey.tm

## 
##    Strata Main Area:
##    __________________
## Design:  systematically spaced transects
## Spacing:  751.2295
## Number of samplers:  26
## Design angle:  0
## Edge protocol:  minus
## Covered area:  778707.5
## Strata coverage: 5.52%
## Strata area:  14108643
## 
##    Strata Morton Lochs:
##    _____________________
## Design:  systematically spaced transects
## Spacing:  218.3674
## Number of samplers:  14
## Design angle:  0
## Edge protocol:  minus
## Covered area:  395665.9
## Strata coverage: 55.32%
## Strata area:  715264.9
## 
##    Study Area Totals:
##    _________________
## Number of samplers:  40
## Covered area:  1174373
## Average coverage: 7.92%

A spacing of 751 m was used in the main stratum and 218 m in the Morton Lochs stratum - these values are calculated based on the stratum areas and should not vary between surveys generated from the same design. You may or may not have achieved the number of transects you requested, this will depend on the random start point calculated for your particular survey. There will also be some variability in coverage, my survey achieved a coverage of 5.7% in the main strata and 64.8% in the Morton Loch strata.

First of all view the design statistics. What is the minimum number of samplers you will achieve in each strata? Is this sufficient to complete separate analyses in each stratum?

sims.tm <- run.coverage(design.tm, reps=100, quiet=TRUE)
sims.tm

## 
##    Strata Main Area:
##    __________________
## Design:  systematically spaced transects
## Spacing:  NA
## Number of samplers:  25
## Design angle:  0
## Edge protocol:  minus
## 
##    Strata Morton Lochs:
##    _____________________
## Design:  systematically spaced transects
## Spacing:  NA
## Number of samplers:  15
## Design angle:  0
## Edge protocol:  minus
## 
## Strata areas:  14108643, 715265
## Region units:  m
## Coverage Simulation repetitions:  100
## 
##     Number of samplers:
##     
##         Main Area Morton Lochs Total
## Minimum      22.0         13.0  37.0
## Mean         24.9         15.0  40.0
## Median       25.0         15.0  40.0
## Maximum      27.0         18.0  43.0
## sd            1.1          1.1   1.5
## 
##     Covered area:
##     
##         Main Area Morton Lochs      Total
## Minimum 685253.11    365433.62 1096006.12
## Mean    765306.60    413011.05 1178317.65
## Median  767279.00    412670.72 1181451.07
## Maximum 818686.53    466013.56 1257491.22
## sd       28739.89     23303.13   34460.53
## 
##     % of region covered:
##     
##         Main Area Morton Lochs Total
## Minimum      4.86        51.09  7.39
## Mean         5.42        57.74  7.95
## Median       5.44        57.69  7.97
## Maximum      5.80        65.15  8.48
## sd           0.20         3.26  0.23
## 
##     Coverage Score Summary:
##     
##          Main Area Morton Lochs     Total
## Minimum 0.00000000    0.2300000 0.0000000
## Mean    0.05430643    0.5739167 0.0792577
## Median  0.05000000    0.6100000 0.0500000
## Maximum 0.13000000    0.7300000 0.7300000
## sd      0.02154755    0.1146747 0.1158266

My design statistics indicated I should achieve between 22 and 27 transects in the main stratum and between 12 and 18 in the Morton Lochs stratum. I might be a bit concerned about the possibility of only achieving 12 transects in the Morton Lochs stratum (remember I cannot just discard a survey due to the number of transects and generate another as it will affect my coverage properties!) but whether this is sufficient will depend on a number of things… what are the objectives of the study? how many detections are you likely to get from each transect? etc. Information from a pilot study would be useful to help decide how many transects are required as a minimum.

Does it appear that you that there is even coverage within strata?

Coverage scores for each strata for the point transect Tentsmuir Forest survey design.

Coverage scores for each strata for the point transect Tentsmuir Forest survey design.

The main strata looks to have even fairly uniform coverage. The values appear to have such small levels of variability that the variability that is seen will be down to stochasticity as it is seen across the entire strata. The Morton Lochs strata we can see has areas of lower coverage around the edge of the study region. This grid is a bit too coarse to allow us to properly judge how much of an issue edge effects will be in this strata. It may be wise to re-run the coverage simulation with a finer coverage grid and more repetitions too. Edge effects could potentially be problematic in such small areas.